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Abstract:

A displacement detecting device includes: a scale which has an optical
lattice; a detecting unit which is disposed so as to be movable in a
scanning direction relative to the scale, inclusive of at least a first
detection portion, a second detection portion and a third detection
portion, arranged in the scanning direction for detecting position
information from the optical lattice; and a calculating portion
configured to obtain a self-calibration curve on graduations of the scale
by specifying positions of the detection portions and calculating
measurement error based on the position information detected by the
detecting unit, wherein: the detecting unit is provided so that a
distance between the first detection portion and the second detection
portion and a distance between the second detection portion and the third
detection portion are different from each other and do not form an
integral multiple.

Claims:

1. A displacement detecting device comprising: a scale which has an
optical lattice; a detecting unit which is disposed so as to be movable
in a scanning direction relative to the scale and which has n(n is an
integer not smaller than 3) detection portions, inclusive of at least a
first detection portion, a second detection portion and a third detection
portion, arranged in the scanning direction for detecting position
information from the optical lattice; and a calculating portion
configured to obtain a self-calibration curve on graduations of the scale
by specifying positions of the detection portions and calculating
measurement error based on the position information detected by the
detecting unit, wherein: the detecting unit is provided so that a
distance between the first detection portion and the second detection
portion and a distance between the second detection portion and the third
detection portion are different from each other and do not form an
integral multiple; and the calculating portion obtains the
self-calibration curve on the graduations of the scale by repeating
operation of moving the detecting unit in the scanning direction until
position information detected by one of the first to third detection
portions is detected by another detection portion, and calculating
measurement error based on the detected position information and a
distance between the detection portions which have detected the position
information.

2. A displacement detecting device according to claim 1, wherein a
difference of the distance between the first detection portion and the
second detection portion from the distance between the second detection
portion and the third detection portion is shorter than a minimum
distance d in which the n detection portions can be arranged physically.

3. A displacement detecting device according to claim 1, wherein the
calculating portion reciprocates the detecting unit in the scanning
direction and acquires the position information.

4. A displacement detecting device according to claim 1, further
comprising a storage unit configured to store the self-calibration curve,
wherein the calculating portion corrects measurement error of the
graduations by referring to the self-calibration curve stored in the
storage unit.

5. A scale calibrating method in a displacement detecting device
including a scale which has an optical lattice, a detecting unit which is
disposed so as to be movable in a scanning direction relative to the
scale and which has n (n is an integer not smaller than 3) detection
portions, inclusive of at least a first detection portion, a second
detection portion and a third detection portion, arranged for detecting
position information from the optical lattice so that a distance between
the first detection portion and the second detection portion and a
distance between the second detection portion and the third detection
portion are not different from each other and do not form an integral
multiple, and a calculating portion configured to obtain a
self-calibration curve on graduations of the scale by specifying
positions of the detection portions and calculating measurement error
based on the position information detected by the detecting unit, the
method comprising: repeating operation of moving the detecting unit in
the scanning direction until position information detected by one of the
first to third detection portions is detected by another detection
portion; obtaining the self-calibration curve on the graduations of the
scale by calculating measurement error based on the detected position
information and a distance between the detection portions which have
detected the position information; and correcting the position
information of the optical lattice by referring to the obtained
self-calibration curve.

6. A scale calibrating program for making a computer execute a scale
calibrating method in a displacement detecting device including a scale
which has an optical lattice, a detecting unit which is disposed so as to
be movable in a scanning direction relative to the scale and which has n
(n is an integer not smaller than 3) detection portions, inclusive of at
least a first detection portion, a second detection portion and a third
detection portion, arranged for detecting position information from the
optical lattice so that a distance between the first detection portion
and the second detection portion and a distance between the second
detection portion and the third detection portion are not different from
each other and do not form an integral multiple, and a calculating
portion configured to obtain a self-calibration curve on graduations of
the scale by specifying positions of the detection portions and
calculating measurement error based on the position information detected
by the detecting unit, the program comprising: repeating operation of
moving the detecting unit in the scanning direction until position
information detected by one of the first to third detection portions is
detected by another detection portion; obtaining the self-calibration
curve on the graduations of the scale by calculating measurement error
based on the detected position information and a distance between the
detection portions which have detected the position information; and
correcting the position information of the optical lattice by referring
to the obtained self-calibration curve.

Description:

BACKGROUND

[0001] 1. Field of the Invention

[0002] The present invention relates to a displacement detecting device, a
scale calibrating method and a scale calibrating program applied to a
linear encoder, a rotary encoder, etc.

[0003] 2. Description of the Related Art

[0004] Generally, measurement error of a displacement measuring device
such as an encoder is evaluated before shipment. A highly accurate
displacement sensor such as a laser interferometer is used for a
reference for error evaluation. The thus obtained error data are shipped
in the form of a pre-shipment inspection table together with the encoder
so as to be used as important data for warranting performance of the
encoder.

[0005] However, the scale of the encoder may be distorted according to the
material and length of the scale and the fixing method when the scale of
the encoder is attached to an application such as a machine tool, a
measuring device, etc. In some cases, non-negligible level measurement
error in regard to a required specification may be caused by the
generated distortion of the scale so that reliability of error data
evaluated in advance will be spoiled.

[0006] As a method for solving this problem, it is thought of that a
reference displacement sensor is set up in a user's application to apply
on-machine calibration to the measurement error of the encoder. It is
however undesirable that a burden is imposed on the user in consideration
of the labor for setting up the displacement sensor and the price of the
highly accurate displacement sensor.

[0007] On the other hand, for example, methods for self-calibration
measurement error on graduations of a scale (JP-A-2008-224578 and
"Satoshi Kiyono, "Intelligent Precision Measurement", The Japan Society
for Precision Engineering, 2009, Vol. 75, No. 1, pp. 89-90") are known in
this type displacement detecting device. Use of these self-calibration
methods permits measurement error of an encoder to be calibrated without
any highly accurate displacement sensor set up in an application.

[0008] However, when configuration is made in such a manner that a
plurality of sensors are arranged at intervals of predetermined distance
as disclosed in JP-A-2008-224578 and "Satoshi Kiyono, "Intelligent
Precision Measurement", The Japan Society for Precision Engineering,
2009, Vol. 75, No. 1, pp. 89-90", the sampling interval of measurement
error becomes equal to the pitch of arrangement of the sensors. For this
reason, measurement error having a period not longer than twice as long
as the arrangement pitch cannot be restored correctly, so that the
frequency of measurement error allowed to be calibrated is limited.

[0009] Although it may be thought of that the pitch of arrangement of the
sensors is narrowed to solve this problem, such a minimum distance that
the sensors do not interfere with one another physically is required as
the arrangement pitch. For this reason, narrowing the pitch of
arrangement of the sensors is limited.

[0010] Moreover, use of a highly accurate displacement sensor such as a
laser interferometer or preparation of a reference sensor or the like is
not desirable because configuration becomes uselessly expensive. When
measurement error of a non-negligible level is caused by distortion of
the scale at the time of mounting or the like, it may be necessary to set
up the reference displacement sensor again and a lot of cost and labor is
still required.

SUMMARY

[0011] The invention is accomplished to solve such a problem and an object
of the invention is to provide a displacement detecting device, a scale
calibrating method and a scale calibrating program which can be formed
easily and inexpensively without any laser interferometer, any reference
scale, etc. so that measurement error on graduations can be calibrated
accurately.

[0012] A displacement detecting device according to the invention
includes: a scale which has an optical lattice; a detecting unit which is
disposed so as to be movable in a scanning direction relative to the
scale and which has n(n is an integer not smaller than 3) detection
portions, inclusive of at least a first detection portion, a second
detection portion and a third detection portion, arranged in the scanning
direction for detecting position information from the optical lattice;
and a calculating portion configured to obtain a self-calibration curve
on graduations of the scale by specifying positions of the detection
portions and calculating measurement error based on the position
information detected by the detecting unit; wherein: the detecting unit
is provided so that a distance between the first detection portion and
the second detection portion and a distance between the second detection
portion and the third detection portion are different from each other and
do not form an integral multiple; and the calculating portion obtains the
self-calibration curve on the graduations of the scale by repeating
operation of moving the detecting unit in the scanning direction until
position information detected by one of the first to third detection
portions is detected by another detection portion, and calculating
measurement error based on the detected position information and a
distance between the detection portions which have detected the position
information.

[0013] In this configuration, the sampling interval which is an interval
for acquiring output data can be set to be shorter than the distance
between detection portions of the detecting unit, so that a
self-calibration curve having finer graduations can be obtained.
Accordingly, measurement error can be corrected accurately by an
inexpensive configuration.

[0014] In one embodiment of the invention, a difference of the distance
between the first detection portion and the second detection portion from
the distance between the second detection portion and the third detection
portion is shorter than a minimum distance d in which the n detection
portions can be arranged physically.

[0015] In another embodiment of the invention, the calculating portion
reciprocates the detecting unit in the scanning direction and acquires
the position information.

[0016] In a further embodiment of the invention, the displacement
detecting device further includes: a storage unit which stores the
self-calibration curve; wherein: the calculating portion corrects
measurement error of the graduations by referring to the self-calibration
curve stored in the storage unit.

[0017] A scale calibrating method according to the invention is a scale
calibrating method in a displacement detecting device including a scale
which has an optical lattice, a detecting unit which is disposed so as to
be movable in a scanning direction relative to the scale and which has
n(n is an integer not smaller than 3) detection portions, inclusive of at
least a first detection portion, a second detection portion and a third
detection portion, arranged for detecting position information from the
optical lattice so that a distance between the first detection portion
and the second detection portion and a distance between the second
detection portion and the third detection portion are not different from
each other and do not form an integral multiple, and a calculating
portion configured to obtain a self-calibration curve on graduations of
the scale by specifying positions of the detection portions and
calculating measurement error based on the position information detected
by the detecting unit, the method including: the detecting step of
repeating operation of moving the detecting unit in the scanning
direction until position information detected by one of the first to
third detection portions is detected by another detection portion; the
calculating step of obtaining the self-calibration curve on the
graduations of the scale by calculating measurement error based on the
detected position information and a distance between the detection
portions which have detected the position information; and the correcting
step of correcting the position information of the optical lattice by
referring to the obtained self-calibration curve.

[0018] A scale calibrating program according to the invention is a scale
calibrating program for making a computer execute a scale calibrating
method in a displacement detecting device including a scale which has an
optical lattice, a detecting unit which is disposed so as to be movable
in a scanning direction relative to the scale and which has n(n is an
integer not smaller than 3) detection portions, inclusive of at least a
first detection portion, a second detection portion and a third detection
portion, arranged for detecting position information from the optical
lattice so that a distance between the first detection portion and the
second detection portion and a distance between the second detection
portion and the third detection portion are not different from each other
and do not form an integral multiple, and a calculating portion
configured to obtain a self-calibration curve on graduations of the scale
by specifying positions of the detection portions and calculating
measurement error based on the position information detected by the
detecting unit, the program including: the detecting step of repeating
operation of moving the detecting unit in the scanning direction until
position information detected by one of the first to third detection
portions is detected by another detection portion; the calculating step
of obtaining the self-calibration curve on the graduations of the scale
by calculating measurement error based on the detected position
information and a distance between the detection portions which have
detected the position information; and the correcting step of correcting
the position information of the optical lattice by referring to the
obtained self-calibration curve.

[0019] According to the invention, it is possible to make configuration
easily and inexpensively so as to be able to calibrate measurement error
on graduations of a scale accurately.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will become more fully understood from the
detailed description given hereinbelow and the accompanying drawing which
is given by way of illustration only, and thus is not limitative of the
present invention and wherein:

[0021] FIG. 1 is a schematic view showing a configuration of a
photoelectric encoder which forms a displacement detecting device
according to an embodiment of the invention.

[0022] FIG. 2 is a view for explaining a basic principle of
self-calibration on graduations of a scale.

[0023] FIG. 3 is a view for explaining the basic principle.

[0024] FIG. 4 is a view for explaining a configuration of a detecting unit
in the photoelectric encoder.

[0025] FIG. 5 is a view for explaining steps in the detecting unit.

[0026] FIG. 6 is a view for explaining operation based on simulation
models of detecting units according to Example of the invention and
Comparative Example.

[0027]FIG. 7 is a view for explaining operation based on the simulation
model of the detecting unit according to Example.

[0028] FIG. 8 is a view for explaining a configuration of a detecting unit
in a photoelectric encoder which forms a displacement detecting device
according to another embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0029] A displacement detecting device, a scale calibrating method and a
scale calibrating program according to embodiments of the invention will
be described below in detail with reference to the accompanying drawings.

[0030] FIG. 1 is a schematic view showing a configuration of a
photoelectric encoder which forms a displacement detecting device
according to an embodiment of the invention. As shown in FIG. 1, the
photoelectric encoder 100 has a scale 10, a detecting unit 20, and a
calculating portion 30. For example, the photoelectric encoder 100 is
formed as a reflective type in this embodiment.

[0031] For example, the scale 10 is constituted by a tape scale and has
position information for detecting positions of measurement points of
detection portions (first to third detection portions) 21, 22 and 23
which form the detecting unit 20. The scale 10 is provided so that light
irradiated from the detection portions 21 to 23 of the detecting unit 20
is reflected toward the detection portions 21 to 23. Incidentally, n (n
is an integer not smaller than 3) detection portions may be provided.

[0032] As shown in FIG. 1, the scale 10 has a rectangular film-like board
11, and a track 12 provided on the board 11. The longitudinal directions
of the board 11 are moving directions (scanning directions X) of the
scale 10 relative to the detecting unit 20 at the time of measurement.

[0033] The track 12 is constituted by patterns 12a. The patterns 12a are
patterns arranged at intervals of a predetermined pitch (e.g. in the
order of μm) along the scanning directions X so that bright portions
or dark portions are arranged periodically.

[0034] The detecting unit 20 is formed so that the detecting unit 20 can
be moved in the scanning directions X relative to the scale 10. The
respective detection portions 21 to 23 detect position information from
the scale 10. For example, the respective detection portions 21 to 23 are
arranged so that the distance between a measurement point of the first
detection portion 21 and a measurement point of the second detection
portion 22 is the minimum physically allocable distance d, and the
distance between a measurement point of the second detection portion 22
and a measurement point of the third detection portion 23 is a distance
αid (αi (i=2, 3, . . . , n-1)) larger than the
minimum distance d. Incidentally, αi is a non-integer constant
larger than 1.

[0035] Specifically, the respective detection portions 21 to 23 irradiate
light onto the scale 10 (track 12) and receive the light reflected from
the scale 10. The detecting unit 20 detects position information of
measurement points of the respective detection portions 21 to 23 based on
the light received by the respective detection portions 21 to 23.

[0036] The calculating portion 30 specifies the positions of the
measurement points of the respective detection portions 21 to 23 based on
the detected position information. The calculating portion 30 calculates
measurement error on graduations of the scale 10 detected by the
respective detection portions 21 to 23 and obtains a precision curve
(self-calibration curve). For example, the calculating portion 30 is
constituted by a built-in CPU of a computer which stores the obtained
self-calibration curve in a storage portion 31, reads a scale calibrating
program from the storage portion 31 and executes the program to thereby
perform a process of correcting measurement error on the graduations of
the scale 10 or achieve various kinds of operations, for example, by
referring to the self-calibration curve.

[0037] FIGS. 2 and 3 are views for explaining a basic principle of
self-calibration on graduations of the scale. As shown in FIG. 2, a
detecting unit 200 having a detection portion 201 and a detection portion
202 disposed side by side along a scale 209 having pitch displacement due
to distortion is prepared first. For example, the distance between
measurement points of the detection portions 201 and 202 is set as d, and
the outputs of the detection portions 201 and 202 are set as m1 (x)
and m2 (x) respectively. Assuming now that f(x) is measurement
error, then the output m1 (x) is given as m1 (x)=x+f (x) and
the output m2 (x) is given as m2 (x)=(x+d)+f (x+d).

[0038] For measurement, the detecting unit 200 is moved (stepwise) at
intervals of a predetermined pitch along a scanning direction X, and the
outputs m1 (x) and m2 (x) of the detection portions 201 and 202
are sampled stepwise. When the number of steps required for scanning the
whole length of the scale 209 is n and the amount of each step given to
the detecting unit 200 is DSTEP, the outputs m1 (DSTEPi)
and m2 (DSTEPi) of the detection portions 201 and 202 at the
i-th step (i=0, 1, . . . , n) are given by the following expressions (1)
and (2) respectively.

[0039] [Numeral 1]

m1 (DSTEPi)=DSTEPi+f(DSTEPi) (1)

[0040] [Numeral 2]

m2 (DSTEPi)=DSTEPi+d+f(DSTEPi+d) (2)

[0041] Accordingly, it is found that the output m2 (DSTEPi) has
an offset of d compared with the output mi (DSTEPi).
Incidentally, the distance d between measurement points of the detection
portions 201 and 202 needs to be obtained by some method in advance.

[0042] When the detecting unit 200 is moved stepwise in one (e.g. in a
rightward direction in the drawing) of the scanning directions X, the
amount of each step is controlled so that the output m1 (DSTEP)
of the detection portion 201 disposed on the rear side in the moving
direction is aligned with the output m2(0) of the detection portion
202 disposed on the one-step preceding side in the moving direction as
shown in FIG. 3. On this occasion, the distance d between measurement
points of the detection portions 201 and 202 is known. Accordingly, when
the output of the detection portion 201 becomes equal to the output of
the detection portion 202 at the preceding step, the amount of each step
becomes equal to the distance d between the measurement points so that
the following expression (3) is established.

[0043] [Numeral 3]

DSTEP=d (3)

[0044] Incidentally, when the detecting unit 200 is moved first stepwise
(in the case of i=1), it is necessary to align the output of the
detection portion 201 with the output of the detection portion 202 at the
initial position. Accordingly, it is desirable that the scale 209 is an
absolute scale but the scale 209 may be an incremental scale according to
the position information detecting method.

[0045] Measurement error f (di) at the i-th step (i=0, 1, . . . , n) can
be expressed as the following expression (4) in accordance with the
aforementioned expressions (1) and (3).

[0046] [Numeral 4]

f(di)=m1(di)-di (4)

[0047] In the aforementioned expression (4), measurement error is
calculated based on the output of the detection portion 201 while the
sampling position is used as a measurement reference. When the output of
the detection portion 201 is acquired and the aforementioned expression
(4) is calculated based on the output after each step is completed,
measurement error f (di) on the whole length of the scale 209 can be
obtained and a self-calibration curve based on the measurement error
f(di) can be obtained.

[0048] Although improvement in accuracy of the encoder can be attained
when this self-calibration curve is used for correcting graduations of
the scale 209, it is impossible to calibrate measurement error of
higher-frequency highly accurate graduations by the configuration of the
aforementioned basic principle because reduction in the distance d
between measurement points is limited. Accordingly, the displacement
detecting device according to this embodiment uses the detecting unit 20
having at least three detection portions for performing self-calibration
as follows.

[0049] FIG. 4 is a view for explaining the configuration of the detecting
unit in the photoelectric encoder. FIG. 5 is a view for explaining steps
in the detecting unit. Although the detecting unit 20 shown in FIG. 1 is
formed to have the first to third detection portions 21 to 23, the
detecting unit 20 can be formed to have a larger number of detection
portions. Accordingly, description will be made here on the assumption
that the detecting unit 20 has n (n is an integer not smaller than 3)
detection portions.

[0050] As shown in FIG. 4, the detecting unit 20 has n detection portions,
that is, first to n-th detection portions 21 to n. The distances between
measurement points of the respective detection portions are set as d,
α2d, α3d, . . . , an-1d in view from the first
detection portion 21 to the n-th detection portion. αi is a
non-integer constant larger than 1 and is calculated in advance.

[0051] First, output data at measurement points of the respective
detection portions 21 to n at an initial position are acquired. Then,
output data at measurement points in the first step are acquired in such
a manner that the detecting unit 20 is moved stepwise in the scanning
direction X while the amount of each step is controlled based on the
output data acquired at the initial position so that, for example, the
output at the measurement point of the first detection portion 21 at the
first step is aligned with the output at the measurement point of the
second detection portion 22 at the initial position.

[0052] Then, output data at measurement points in the second step are
acquired in such a manner that the detecting unit 20 is moved stepwise
likewise while the amount of each step is controlled based on the output
data acquired at the first step so that, for example, the output at the
measurement point of the first detection portion 21 at the second step is
aligned with the output at the measurement point of the second detection
portion 22 at the first step.

[0053] Output data at measurement points in the third step are further
acquired in such a manner that the detecting unit 20 is moved stepwise
likewise while the amount of each step is controlled based on the output
data acquired at the initial position so that, for example, the output at
the measurement point of the first detection portion 21 at the third step
is aligned with the output at the measurement point of the third
detection portion 23 at the initial position.

[0054] When the detecting unit 20 is moved stepwise while the amount of
each step is controlled based on the output data acquired at the
measurement points of the second to n-th detection portions 22 to n in
accordance with each step so that, for example, the output at the
measurement point of the first detection portion 21 is aligned with those
at the measurement points of the second to n-th detection portions 22 to
n in this manner, a region in which the sampling interval is shorter than
the distance d (e.g. the interval (α2-1)d<d) appears.

[0055] Moreover, when the aforementioned step is repeated on the whole
length of the scale, a sampling interval shorter than the distance d can
be obtained at random. Therefore, though configuration is made so that
the distances between measurement points of the respective detection
portions 21 to n are all not shorter than d, measurement error can be
calculated at a sampling interval not longer than d and a
self-calibration curve can be obtained to correct position information of
the scale.

[0056] Although measurement references for calculating measurement error
are sampling positions, all the sampling positions can be calculated back
based on the known measurement point distances d to αn-1d. In
this manner, the displacement detecting device according to this
embodiment can be formed without any expensive configuration so that
measurement error of graduations can be calibrated easily, inexpensively
and accurately.

[0057] The aforementioned configuration will be described below
specifically according to Example. FIG. 6 is a view for explaining
operation based on simulation models of detecting units according to
Example of the invention and Comparative Example. FIG. 7 is a view for
explaining operation based on the simulation model of the detecting unit
according to Example.

[0058] As shown in FIG. 6, the detecting unit 20 according to Example has
such three detection portions that the distance d between measurement
points of the first detection portion 21 and the second detection portion
22 is set to be 10 mm and the distance α2d between measurement
points of the second detection portion 22 and the third detection portion
23 is set to be 12.5 mm.

[0059] On the other hand, the detecting unit 20A according to Comparative
Example has such two detection portions that the distance d between
measurement points of the first detection portion 21 and the second
detection portion 22 is set to be 10mm. Accordingly, the detecting unit
20 is formed so that the aforementioned parameters satisfy n=3, d=1 and
α2=1.25 whereas the detecting unit 20A is formed so that the
aforementioned parameters satisfy n=2 and d=1.

[0060] Obtained sampling positions are simulated on 100 mm in such a
manner that each detecting unit 20 or 20A is moved stepwise so that the
output at the measurement point of the first detection portion 21 is
aligned with the output at the measurement points of the second and third
detection portions 22 and 23. As a result, it is obvious that the
sampling interval in the detecting unit 20 according to Example is 2.5 mm
from the moving region after 60 mm whereas the sampling interval in the
detecting unit 20A according to Comparative Example is 10 mm on the whole
region.

[0061] This indicates that the sampling interval in Example is one fourth
as long as the sampling interval in Comparative Example. That is, this
indicates that measurement error can be calculated at sampling intervals
of 10 mm or shorter even if the distance between measurement points is 10
mm or longer. Accordingly, measurement error of graduations can be
calibrated accurately compared with Comparative Example.

[0062] Incidentally, in the example shown in FIG. 6, the sampling interval
in Example is not always 2.5 mm in the moving region of 0 to 60 mm.
Accordingly, it is obvious that higher accuracy can be further attained.
It is therefore desirable that configuration is made in such a manner
that the detecting unit 20 is reciprocated in the detection range of the
scale 10 to add sampling positions as shown in FIG. 7.

[0063] Specifically, sampling positions are obtained in a forward path in
the aforementioned manner and sampling positions are added in a backward
path in such a manner that the detecting unit 20 is moved stepwise so
that, for example, the output at the measurement point of the third
detection portion 23 is aligned with the outputs at the measurement
points of the first and second detection portions 21 and 22 obtained in
the forward path. In this manner, the sampling interval can be set to be
2.5 mm on the whole length in the detection range of the scale.

[0064] Although the embodiment of the invention has been described above,
the invention is not limited thereto but various changes, additions, etc.
may be made without departing from the gist of the invention. For
example, the photoelectric encoder may be a linear type or a rotary type.
As shown in FIG. 8, at least three detection portions 21, 22 and 23 of
the detecting unit 20 may be made of one photo acceptance element array
separated into at least three photo acceptance regions so that, for
example, distances d to αn-1d (d and α2d in FIG. 8)
between measurement points are formed as described above. Further, the
invention can be applied not only to an incremental scale having a
periodic optical lattice but also to an absolute scale having a
pseudo-random code pattern and a multi-track scale having both or either
of these scales.